The cryo-EM determination of atomic structures by single-particle methods represents a revolution in structural biology. The method relies on the astonishing ability of numerical computations to yield high- resolution density maps from collections of extremely noisy ?particle? images. This ability however carries with it a real danger of spurious results emerging from the black box of image-processing and reconstruction software. We propose to develop an educational curriculum including video, software and an e-book that provides a rigorous treatment of the mathematical foundations of cryo-EM image processing and reconstruction. The goal of our instructional efforts is to ground students and researchers in the understanding of the principles and best-practice methods in the computational processing that leads to molecular structures.